A firm has seven projects to choose from. Since the firm does not have the capital budget to do all the projects.

A firm has seven projects to choose from. Since the firm does not have the capital budget to do all theprojects, rank each by IRR. If the firm’s capital budget is $70,000, which projects will be funded? What
will the firm’s MARR be?
Internal Rate of return (IRR) is the rate at which the NPV of all future cash flows equals zero
IRR(project1) = 17.68%
IRR(project2) = 14.28%
IRR(project3) = 14.16%
IRR(project4) = 21.59%
IRR(project5) = 15.03%
IRR(project6) = 18.45%
IRR(project7) = 16.30%
Thus, ranking them according to IRR, we have 4>6>1>7>5>2>3
Capital Budget = 70000. Thus, the person will invest in 4 (20000) + 6 (15000) + 1 (10000) + 7 (25000) =
70000
The MARR would be the rate of return on the project with the lowest IRR. Because of this, even though
that project would be zero profits, all others would be earning higher profits
Thus, MARR = 16.30%. If MARR is higher than this, then the last project (7) would not be undertaken as
it would have negative future cash flows
The ABC Company may buy a heat exchanger for $80,000 installed. If their cost of money is 8% and the
exchanger has a useful life of 8 years, what must the annual benefit of the exchanger be in order for ABC
Company to break even on this purchase?
Present Value = $80,000
Useful Life = 8 years
Cost of money = 8%
The annual benefit that will just break even the purchase will be the annual receipt at which NPV equals
zero. In short, it will be annuity of 8 years @8% with present value = $80,000
Formula neededEAC = Equated Annual Cost = (Present Value) X ((i X (1+i)^n)/((1+i)^n-1)) + Annual
Maintenance cost – (Future Value) X (i/(1+i)^n-1)
5 years
Project
A
B
C
D
E
F
First Cost Net Benefits IRR
$ 10.000 $
3.200
$ 68.000 $
22.000
$ 20.000 $
6.000
$ 45.000 $
12.000
$ 15.000 $
5.000
$ 5.000 $
2.000
18%
19%
15%
10%
20%
29%
Project
F
E
B
A
C
D
First Cost Net Benefits IRR
$ 5.000 $
2.000
$ 15.000 $
5.000
$ 68.000 $
22.000
$ 10.000 $
3.200
$ 20.000 $
6.000
$ 45.000 $
12.000
29%
20%
19%
18%
15%
10%
5 years
I = 10%
Project
A
B
C
D
E
F
First Cost
Net Benefits IRR
$ 10.000 $
3.200
$ 68.000 $
22.000
$ 20.000 $
6.000
$ 45.000 $
12.000
$ 15.000 $
5.000
$
5.000 $
2.000
PW
18% $2.130,52
19% $15.397,31
15% $2.744,72
10%
$489,44
20% $3.953,93
29% $2.581,57
$100.000
Project
B
E
C
F
A
D
PW
$15.397,31
$3.953,93
$2.744,72
$2.581,57
$2.130,52
$489,44
profit
$19.351,24
Project
F
E
B
A
C
D
IRR
29%
20%
19%
18%
15%
10%
$24.063,33
Project
F
E
B
A
C
D
First Cost Net BenefitsIRR
$ 5.000 $ 2.000
$ 15.000 $ 5.000
$ 68.000 $ 22.000
$ 10.000 $ 3.200
$ 20.000 $ 6.000
$ 45.000 $ 12.000
29%
20%
19%
18%
15%
10%
IRR
F
30
25 E
20
15
10
5
0
20000
B
A
C
D
40000
60000
80000
100000
120000
140000
160000
Cumulative Investment
Project
F
E
B
A
C
D
First Cost Net BenefitsIRR
$ 5.000 $ 2.000
$ 15.000 $ 5.000
$ 68.000 $ 22.000
$ 10.000 $ 3.200
$ 20.000 $ 6.000
$ 45.000 $ 12.000
Cumulative Investment
11% $
5.000
20% $
20.000
19% $
88.000
18% $
98.000
15% $ 118.000
10% $ 163.000
Projects F,E,B,A should be undertaken
MARR =18%
3 years
Project First Cost Annual Benefit PW @ 15% IRR
3 $ 10.000 $
6.000 $
3.699
1 $ 20.000 $
11.000 $
5.115
7 $ 40.000 $
21.000 $
7.948
5 $ 25.000 $
13.000 $
4.682
4 $ 5.000 $
2.400 $
480
2 $ 30.000 $
14.000 $
1.965
6 $ 15.000 $
7.000 $
983
36%
30%
27%
26%
21%
19%
19%
3 years
Project
First Cost Annual Benefit
PW @ 15% IRR
3 $ 10.000 $ 6.000 $ 3.699
1 $ 20.000 $ 11.000 $ 5.115
7 $ 40.000 $ 21.000 $ 7.948
5 $ 25.000 $ 13.000 $ 4.682
4 $ 5.000 $ 2.400 $
480
2 $ 30.000 $ 14.000 $ 1.965
6 $ 15.000 $ 7.000 $
983
Invest in project 3,1,7
MARR = 27%
Cumulative Investment
36% $
10.000
30% $
30.000
27% $
70.000
26% $
95.000
21% $
100.000
19% $
130.000
19% $
145.000
10 years
Project
C
B
D
E
A
First Cost Annual Benefit IRR
Cumulative Investment
10000
2400
20,18%
10000
20000
4200
16,40%
30000
30000
6200
15,97%
60000
40000
7600
13,77%
100000
15000
2800
13,32%
115000
C,B, and D
MARR = 16%
80000 initial investment
8 year life
8%
annual savings???
($13.921,18)
first cost
6 years
O&M
i=8%
$3.563,15
10000
1400
i=5%
first cost
O&M cost
neighborhood disbenefit
t
$27.036,39
150000
5000
10000
20
initial cost
annual cost
research time
revs start year after end of research time
Rev
i=
horizon
research time
200000
300000
???
550000
10%
20
Total Costs
Total Revenue
Net
1
($472.727,27) $ 3.802.236,41
$3.329.509,13
2
($720.661,16) $ 3.314.691,45
$2.594.030,29
3
($946.055,60) $ 2.939.034,05
$1.992.978,45
4 ($1.150.959,63) $ 2.597.527,32
$1.446.567,69
5 ($1.337.236,03) $ 2.287.066,66
$949.830,63
6 ($1.506.578,21) $ 2.004.829,70
$498.251,49
7 ($1.660.525,65) $ 1.748.250,64
$87.724,99
7,2 ($1.689.593,24) $ 1.699.804,65
$10.211,41
8 ($1.800.477,86) $ 1.514.996,95
($285.480,91)
9 ($1.927.707,14) $ 1.302.948,14
($624.759,01)
10 ($2.043.370,13) $ 1.110.176,49
($933.193,64)
11 ($2.148.518,30) $
934.929,54 ($1.213.588,76)
12 ($2.244.107,55) $
775.614,13 ($1.468.493,41)
13 ($2.331.006,86) $
630.781,94 ($1.700.224,92)
Init Cost
time
i
3000000
15
10%
Principal % change Payment
-10% $354.979,20
-5% $374.700,26
0% $394.421,33
5% $414.142,40
10% $433.863,46
Interest rate change Payment
-20% $350.488,63
-10% $372.176,65
0% $394.421,33
10% $417.195,72
20% $440.472,72
Time
Payment
10 $488.236,18
15 $394.421,33
20 $352.378,87
25 $330.504,22
30 $318.237,74
Factor
% Base Case
PW
Spiderplot of PW
BC
$1
EC
$1
AR
S
$1
i
N
Base Case
$1
100%
$0
$0
$0%
20%
40%
60%
Spiderplot of PW
BC
EC
AR
S
i
N
Base Case
80%
100%
120%
To use template replace variable names, min, and max values.
Variable First Cost Final Cost
Annual
Annual
name
benefit
benefit
min 9157.00
6841.00
5036.00
5036.00
max 10157.00 12473.00 21209.00 21209.00
range 1,000.00
5,632.00 16,173.00 16,173.00
spacer
9157.00
6841.00
5036.00
5036.00
color
1,000.00
5,632.00 16,173.00 16,173.00
color min